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Step * of Lemma rlog_functionality_wrt_rless

∀x,y:{t:ℝ| r0 < t} .  ((x < y) ⇒ (rlog(x) < rlog(y)))
BY
{ (InstLemma `derivative-implies-strictly-increasing` [⌜(r0, ∞)⌝;⌜λ2x.rlog(x)⌝;⌜λ2x.(r1/x)⌝]⋅ THEN Auto) }

1
.....antecedent..... 
(r1/x) continuous for x ∈ (r0, ∞)

2
1. x : {x:ℝ| x ∈ (r0, ∞)} 
⊢ r0 < (r1/x)

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Latex:

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Latex:
\mforall{}x,y:\{t:\mBbbR{}|  r0  <  t\}  .    ((x  <  y)  {}\mRightarrow{}  (rlog(x)  <  rlog(y)))


By

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Latex:
(InstLemma  `derivative-implies-strictly-increasing`  [\mkleeneopen{}(r0,  \minfty{})\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.rlog(x)\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.(r1/x)\mkleeneclose{}]\mcdot{}
  THEN  Auto
  )

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